Deflection of Tubing Under Compression

Run a cable down the center of the tube. Tension in the cable will "reinforce" the tube and work against any buckling tendencies.

You can't run guy wires on the outside?

And, it really doesn't matter much if you start with some deflection. You are probably way over the buckling limit anyway, depending on the wire tension.

I calculate the deflection of 1.5" sch 40 aluminum pipe at approximately 0.5"

That's what I (originally) got with a different calculation than standard beam calcs. But I thought I was using the wrong equation.

What kind of force do you think will be developed between the posts?

Or thinking conversely, how much (displacement) do you think the posts will bend inwards when loaded?

Your question leaves me wondering if you have used the correct calculation. First point is that the self weight of the beam you are using will cause it to sag in the middle. A small value like 0.008" may well be right.

However the critical issue is the compression load that the vertical posts will force into this beam when the wire supporting the vines is loaded/tensioned and soil movement causes/allows the tops of the posts to move inward.

This is a Euler column buckling issue - worst case giving the most conservative answer would be to treat the horizontal beam as being pinned at the ends, best case is to treat the beam as having built in ends. Look up the formulae, I can't remember them off the top of my head.

A crude check would be to be take an assumed compression load in lbs and multiply it by a small assumed initial set in the beam - say 0.2 inches. This will give a bending moment "M" in (say) lb inches that the beam must resist. Then calculate the bending moment capacity of the beam using M = SZ where S is the yield stress in lbs/in2, and Z is the section modulus of the beam in in3. If the M you have generated with a (say) 0.2" bend is way less than the M you can sustain its probably OK.... and you might move on to do a proper check.

The error in the above method is that it assumes that enough side force will elastically build up quick to stop further buckling before the side moment is more than about 0.2". All this is a Euler related issue. Euler properly checks that the resisting moment in the beam builds up more quickly than the bending moment grows as the flexing of the column causes more bending moment arising out of the compression force.

A quick way to assess Z for a typical hollow rectangular tube is to treat the upper and lower edges/areas of the tube as doing all the work and adding say 10-20 percent to allow for what the side area/s do. For a 1 inch square tube 0.125 thick that would be 1 x 0.125 x 0.875 x 1.2 i.e. the area of one side by the distance between their centres of area by a fudge factor to allow for a contribution by side aluminium area/s. If the above is a little confusing, another way to look at it is to use double the area (that is the for each side x 2 ), but with the distance to the centre of the beam cross-section rather than the other side (which is half as big)....so the mathematical result is the same.

All the above work for other units AS LONG AS the same units system is used for length, area, stress and bending etc. through out.

Have you considered filling the round posts with concrete to strengthen them and prevent the flex? you might also try putting a spring at the end of the wire to attach it to the post and use it to tension your wirews.

The weight from the vines will generate considerable tension in the wires. Why not use 3 wood posts at each end arranged in Z (laying on it's side) fashion. (Look at field fences for an example). The cross brace runs from the base of the inner post to the top of the outer post. Use a couple of loops of wire with a Spanish Windless to tension it.

Or run the brace from the top of one to the top of the other with a diagonal wire grace to hold it together.

Don't need the pipe to keep them from leaning towards each other due to the tension of the wire. Use a guide wire to the ground at each post. A commercial guide wire anchor for say a telephone pole. Its a long eye bolt with a large paddle like screw at the end. It screws into the ground. Adjusting the tension between the wire between post and the guide wires will keep the post from leaning.

A GA from me. Always attempt to provide structural stability using tension devices.

good answer!!! tensile stays ARE the answer!!

Nowhere have I seen any reference to windload. Do you experience winds? ... because when your folliage is full the effect will be a signifcant factor.

ururk: How is your horizontal tube loaded? To be able to analyze your beam, we need to know the applied loads. You would need to explain what is attached to your beam, how much load is applied at each point, and the location of each applied load. You mention wires without explaining anything about them.

To estimate applied loads, keep in mind that a lightweight container containing 1 liter of water has a mass of 1 kg, and has a weight of 9.81 N. You could use this for comparative purposes to estimate wire pretension, if any, and to estimate the weight of the portion of a fully-grown, wet plant that will be applied to your beam. You might also want to consider maximum wind loads. Also consider rain. Explain all applied loads, and their location dimensions on your aluminum tube. Are there guy wires on the outside of the upright poles, or not?

I'll create a drawing and try to estimate the loads to the best of my knowledge.